Related papers: Presenting Profunctors
Explaining deep learning model inferences is a promising venue for scientific understanding, improving safety, uncovering hidden biases, evaluating fairness, and beyond, as argued by many scholars. One of the principal benefits of…
We are checking the closed categories beginning with the category of sets and ending with the category of categories. The novelty is a generalizing the notion of adjoint functors to the joint pair of functors in the category of directed…
This thesis investigates effectful declarative programming with an emphasis on non-determinism as an effect. On the one hand, we are interested in developing applications using non-determinism as underlying implementation idea. We discuss…
In this paper we show how the abstract behaviours of higher-order systems can be modelled as final coalgebras of suitable behavioural functors. These functors have the challenging peculiarity to be circularly defined with their own final…
We develop a theory of curved A-infinity-categories around equivalences of their module categories. This allows for a uniform treatment of curved and uncurved A-infinity-categories which generalizes the classical theory of uncurved…
We investigate categories in which products distribute over coproducts, a structure we call doubly-infinitary distributive categories. Through a range of examples, we explore how this notion relates to established concepts such as…
When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of…
We develop a 2-dimensional version of accessibility and presentability compatible with the formalism of flat pseudofunctors. First we give prerequisites on the different notions of 2-dimensional colimits, filteredness and cofinality; in…
Monoidal computer is a categorical model of intensional computation, where many different programs correspond to the same input-output behavior. The upshot of yet another model of computation is that a categorical formalism should provide a…
The humble $\dagger$ ("dagger") is used to denote two different operations in category theory: Taking the adjoint of a morphism (in dagger categories) and finding the least fixed point of a functional (in categories enriched in domains).…
A folklore result in category theory is that a (weakly) Cartesian closed category with finite co-products is distributive. Usually, the proof of this small result is carried on using the fact that the exponential functor is right adjoint to…
We give an introduction to constructive category theory by answering two guiding computational questions. The first question is: how do we compute the set of all natural transformations between two finitely presented functors like…
We describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to…
We study categories whose objects are the braid representations, i.e. strict monoidal functors $F\colon B\rightarrow Mat$ from the braid category $B$ to the category of matrices $Mat$. Braid representations are equivalent to solutions to…
Query Containment Problem (QCP) is one of the most fundamental decision problems in database query processing and optimization. Complexity of QCP for conjunctive queries (QCP-CQ) has been fully understood since 1970s. But, as Chaudhuri and…
The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be…
The well-known difficulties arising in a classification which is not set-theoretically trivial---involving what is sometimes called a non-smooth quotient---have been overcome in a striking way in the theory of operator algebras by the use…
We present a domain-specific type theory for constructions and proofs in category theory. The type theory axiomatizes notions of category, functor, profunctor and a generalized form of natural transformations. The type theory imposes an…
Inductive and coinductive types are commonly construed as ontological (Church-style) types, denoting canonical data-sets such as natural numbers, lists, and streams. For various purposes, notably the study of programs in the context of…
Cartesian differential categories come equipped with a differential combinator that formalizes the directional derivative from multivariable calculus. Cartesian differential categories provide a categorical semantics of the differential…